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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.08419 |
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| _version_ | 1866917951542657024 |
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| author | Lombardi, Luigi |
| author_facet | Lombardi, Luigi |
| contents | We show that any equivalence of bounded derived categories of coherent sheaves on a smooth projective complex variety supported in a closed algebraic subset preserves the dimension of the support in two cases: (i) the restriction of the (anti)canonical bundle to the support is ample; (ii) the supports are irreducible and the equivalence sends a skyscraper sheaf of a closed point to a skyscraper sheaf of a closed point. Moreover, in the first case the equivalence recovers the set of closed points of the support up to homeomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08419 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reconstruction theorems in the supported case Lombardi, Luigi Algebraic Geometry We show that any equivalence of bounded derived categories of coherent sheaves on a smooth projective complex variety supported in a closed algebraic subset preserves the dimension of the support in two cases: (i) the restriction of the (anti)canonical bundle to the support is ample; (ii) the supports are irreducible and the equivalence sends a skyscraper sheaf of a closed point to a skyscraper sheaf of a closed point. Moreover, in the first case the equivalence recovers the set of closed points of the support up to homeomorphism. |
| title | Reconstruction theorems in the supported case |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2503.08419 |